Date: Mar 15, 2013 6:06 PM
Author: Virgil
Subject: Re: Matheology � 224

In article 
<37f8b921-a2db-46d0-a942-2d2ae5b727a3@k14g2000vbv.googlegroups.com>,
William Hughes <wpihughes@gmail.com> wrote:

> On Mar 14, 10:32 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> <snip>
>

> >... consider the list of finite initial segments of natural numbers
> >
> > 1
> > 1, 2
> > 1, 2, 3
> > ...
> >
> > According to set theory it contains all aleph_0 natural numbers in its
> > lines. But is does not contain a line containing all natural numbers.
> > Therefore it must be claimed that more than one line is required to
> > contain all natural numbers. This means at least two line are
> > necessary. There are no special lines necessary, but there must be at
> > least two. In this case, however, we can prove, by the construction of
> > the list, that every union of a pair of lines is contained in one of
> > the lines. This contradicts the assertion that all natural numbers
> > exist and are in lines of the list.

>
>
> Nope.
>
> Nope, two lines are necessary but not sufficient.
>
> Two lines can never do a better job than 1.
>
> Any finite number of lines is necessary but not sufficient.
>
> Any finite number of lines can never do a better job than 1.
>
> An infinite number of lines is necessary and sufficient
>
> An infinite number of lines can do a better job than 1
>
> [In potential infinity things go
>
> Any number of findable lines is not sufficient
>
> An unfindable line is necessary and sufficient
>
> An unfindable line can do a better job than
> any number of findable lines.


Or it would if you could find it.
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